# High School Mathematics for College Liberal Arts

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Suggested Prerequisites

Algebra 1, Geometry

Description

Get ready to apply your math skills to real-world problems. This course gives you the opportunity to explore a range of mathematical concepts and fields, all while connecting ideas to their application in your world. Major topics in this course include linear and exponential functions, geometry in the real world, analysis of data and probability, and the use of functions as models. Logic and theory as they apply to the practical use of mathematical concepts are introduced. You will gain an understanding of how the principles of higher-level math connect to everyday life.

Module One: Linear and Exponential Functions

-solve and graph problems with linear functions

-interpret key features of linear functions

-determine constraints using a real-world context

-interpret key features of exponential functions

-classify exponential functions as growth or decay

-write exponential functions given multiple representations

-graph an exponential function given multiple representations

-determine the constant percent rate of change

Module Two: Utilizing Functions

-compare key features of functions given multiple representations

-determine the best model given a real-world context

-compare simple, compound, and continuously compounded interest

-solve real-world problems involving interest

-explore linear growth and simple interest

-explore exponential growth and compound interest

-explore exponential growth and continuously compounded interest

Module Three: Transformations and Applications of Geometry

-solve problems involving congruence in two-dimensional figures

-solve problems involving similarity in two-dimensional figures

-determine symmetries of transformations of geometric figures

-solve problems with right triangles using trigonometric ratios

-solve problems with right triangles using the Pythagorean Theorem

-solve problems involving area of two-dimensional figures

-solve problems involving surface area of three-dimensional figures

-solve problems involving volume of three-dimensional figures

-determine how dilations affect two-dimensional figures

-determine how dilations affect three-dimensional figures

Module Four: Modeling and Analyzing Data

-determine if given data is numerical or categorical

-determine if given data is univariate or bivariate

-represent a data set using a visual model

-interpret data given a visual model

-compare the appropriate measures of center

-compare the appropriate measures of variability

-note features about the shape of data distributions

-fit a linear function to bivariate numerical data

-fit an exponential function to bivariate numerical data

-solve real-world problems using linear or exponential models

Module Five: Exploring Events Using Probability

-analyze sets, subsets, power sets, and equivalent sets

-explore set relationships using Venn diagrams

-apply Venn diagrams to make arguments about sets

-describe unions, intersections, and complements as subsets

-determine the independence of events using probability

-create two-way tables to organize data

-determine relative, joint, and marginal frequencies

-calculate the conditional probability of two events

-interpret probabilities given a real-world context

-apply the addition and multiplication rules for probability

Module Six: Making Sense of Logic and Theory

-perform set operations and prove set relations

-determine truth values of simple and compound statements

-interpret conditional, biconditional, and quantified statements

-find the converse, inverse, and contrapositive of a statement

-represent logic operations using logical symbolism

-solve problems using logic operations

-determine whether two propositions are logically equivalent

-construct valid arguments using the laws of logic

-give counterexamples to disprove statements

-calculate permutations and combinations as appropriate